Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Thursday, January 04, 2007

Solving Puzzles

An economist, a physicist and a computer scientist were sitting at a
table. A true story, not the beginning of a joke. One of them said

We were solving fundamental problems twenty to thirty years
ago. There is still much we don't understand but today we are only
solving puzzles.

Any one of them could have said that,
scientific insecurity runs through all fields. A similar set of
scientists probably had a similar discussion twenty years ago as well.

At the end they all concluded that the future of their fields lied not
in the cores of their fields but in the interaction between them and
other fields not represented, like biology. They probably also said
that twenty years ago.

13 comments:

I guess the intended meaning here was not that there aren't fundamental unanswered questions, but that no progress is being made on them. For economics, in particular: pardon my ignorance, but what fundamental question has been answered?

"Puzzle" is undeniably a good thing. But can the science-technology ecosystem stably maintain itself with puzzle solvers as the keystone species?

E.g., "sea otters" are wonderful animals; beautiful and free. Yet for infant sea otters to survive, an abundance of kelp and abalone must be present too.

It makes no sense to ask which species is most important, the mobile sea otters or the sessile kelp and abalone. The correct description is "all are essential to the health of the ecosystem."

My reading of Lance's post is that the economists, physicists, and computer scientists are beginning to appreciate that the global science and technology ecosystem is drifting toward what aviation engineers call the coffin corner.

This is a flight regime in which (metaphorically speaking) we've achieved plenty of altitude and speed, but in consequence, are now flying so high and fast that we have very little maneuvering margin.

Which on a planet with six billion people, is not a good operating regime.

John von Neumann both foresaw technology's entry into the coffin corner, and described--in principle--how to safely back out of it, in his 1955 essay Can We Survive Technology?: "All this will merge each nation's affairs with those of every other, more thoroughly than the threat of a nuclear or any other war would have done. \ldots What safeguard remains? Apparently only day-to-day---or perhaps year-to-year---opportunistic measures, a long sequence of small, correct decisions. And this is not surprising. After all, the crisis is due to the rapidity of progress, to the probable further acceleration thereof, and to the reaching of certain critical relationships. Specifically, the effects that we are now beginning to produce are of the same order of magnitude as `the great globe itself.' Indeed, they affect the earth as an entity. Hence further acceleration can no longer be absorbed as in the past by an extension of the area of operations."

The point being, that (hopefully) the economist, the physicist, and the mathematician were not just kvetching, but were having a very serious discussion.

You solve a puzzle, and then, you have not really gained any understanding of anything except of the problem itself.

I have worked on plenty of puzzle-like problems. Some "feel right"; others are also fun to think about but ultimately leave the solver with a sense of emptiness. Some, I feel, advance my knowledge: they somehow fill a small gap in my mental picture of the world. Others are merely what I call "exercise for the brain muscles".

This conundrum is easily explained. The speaker is trying to come to terms with the fact that his work to date has been rather lacklustre, by arguing that he narrowly missed out on some golden age of research in his field. (He is probably in his mid-30s.)

Anonymous said: The speaker is trying to come to terms with the fact that his work to date has been rather lacklustre, by arguing that he narrowly missed out on some golden age of research in his field.

According to Dirac, the speaker's complaint is valid: "A golden era occurs when ordinary people can make extraordinary contributions."

To the extent that our planet is presently not in a golden era, it is valid to ask: Why not? What's missing? Can we supply it?

Admittedly, these questions are dauntingly multidisciplinary. On the other hand, has there ever been a better era in which to do multidisciplinary work?

What astounding quiescence on Lance's important topic, which can be approached from so many ways, and therefore, offers so much scope for creativity, and yes, advancing the goals of the science, math, and technology community.

• Artisticly, from Borges' story Averroes' Dream: "In Alexandria there is a saying that only the main who has already committed a crime and repented of it is incapable of that crime; to be free of an erroneous impression, I myself might add, one must at some time have professed it."

• Economically, from today's New York Times Story on research budgets (page 19, see especially the funding graph entitled "Flatlining Research").

• Strategically, in the form of the President's speech tomorrow on the Iraq War, which will include a major initiative on job creation. And yet, how many people have real confidence that this vital part of the plan will work, both in Iraq and globally?

Hasn't what Simon Ramo famously said of system engineering in 1984 become equally true of computational complexity theorists today?

• Simon Ramo: "[Complexity theory] is the [understanding] of the whole, as distinguished from the understanding of the parts. ... The principle tools of the [complexity theorist] are the human brain, the electronic computer, and numerous mathematical analysis techniques. ... We should anticipate the use of the techniques of [complexity theory] on an even wider range of problems than any of the past. ... Making decisions as correctly as possible under trying circumstances is a critical portion of [complexity theory]."

Time to close out this thread (since I'm pretty much the only poster, too bad!).

Lance's remark "scientific insecurity runs through all fields" is IMHO a good example of a "Niels Bohr truth", that is, a truth whose opposite is also a great truth.

So let's consider what it might mean to say the opposite, that "confidence runs through all scientific fields".

To name a few confident epochs of the past century in (roughly) chronological order: special relativity, quantum mechanics, general relativity, radar, computing machines, information theory, condensed matter physics, molecular biology, space travel, VLSI technology, cryptography, immunology, genomics, proteomics ... many more could me named (and the preceding list is notably sparse in mathematics, most particularly in geometry, which reflects my own ignorance).

One thing these epochs obviously have in common is, each is associated with a confident beginning to a new scientific discipline. And with specific reference to the "puzzle-solving" complaint of the economist, physicist, and computer scientists of Lance's post, each of these epochs is a successful (but always temporary, alas!) escape from "puzzle solving" into an era of scientific creativity, economic prosperity, and abundant academic jobs.

Obviously, one of the main keys to scientific success---especially for young people---is the knack for allying early-on with the next efflorescence of scientific confidence. This hard-to-define skill partakes equally of intelligence, creativity, persistence, discipline, team-building ability, and luck (because as Yogi Berra said "Prediction is very hard, especially about the future").

We see that the talents needed to predict the future are pretty much identical to the talents needed to create that future. Which implies the following harsh conclusion: predicting the future with accuracy entails an implicit responsibility to create that future.

No blog-poster, including me, would wish to accept that responsibility and/or that possibility of failure! To escape it, we will construct a meta-prediction. Substituting "<your discipline>" for "system engineering" in Simon Ramo's famous essay, we obtain a pretty good Niels Bohr truth, which spreads responsibility for creating the future pretty much equally across all scientific disciplines, and across old and young alike:

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Escaping Puzzle-Solving(after Simon Ramo)

<your discipline> is the [understanding] of the whole as distinguished from the [understanding] of the parts. <your discipline> harmonizes optimally an ensemble of subsystems and components [that are] related by channeled flows of information, mass, and energy. ... The principle tools of <your discipline> are the human brain, the electronic computer, and numerous mathematical analysis techniques. ... We should anticipate the use of the techniques of <your discipline> on an even wider range of problems than any of the past. ... Two major trends may be expected in <your discipline>. First, the capabilities of the analytical tools of <your discipline> will continue to increase. ... The second major trend is the increase in the complexity of systems being [understood]. ... We should anticipate the use of the techniques of <your discipline> on an even wider range of problems than any of the past.